Question

# 12.Vertices仕6, 0), foci ± 4,0)

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Solution

## The given vertices of ellipse are (±6,0) and foci are (±4,0) .(1) Since the vertices are on the x axis, so the equation of the ellipse is represented as x 2 a 2 + y 2 b 2 =1 ,where x is the major axis. Vertices of ellipse are represented as ( ±a,0 ) when x is the major axis.(2) Compare vertices in equation (1) and (2) a=6 Foci of ellipse are represented as ( ±c,0 ) when x is the major axis. (3) Compare foci in equation (1) and (3) c=4 Substitute values of a and c to determine b .Also, c 2 = a 2 − b 2 4 2 = 6 2 − b 2 b 2 =36−16 b = 20 Equation of ellipse is x 2 6 2 + y 2 ( 20 2 ) =1 Therefore, the equation of ellipse with vertices ( ±6,0 ) and foci ( ±4,0 ) is x 2 36 + y 2 20 =1 .

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